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In this paper, a flux difference lattice hydrodynamics model is extended by considering the traffic jerk effect which comes due to vehicular motion of non-motor automobiles. The effect of traffic jerk has been examined through linear stability analysis and shown that it can significantly enlarge the unstable region on the phase diagram. To describe the phase transition of traffic flow, mKdV equation near the critical point is derived through nonlinear stability analysis. The theoretical findings have been verified using numerical simulation which confirms that the jerk parameter plays an important role in stabilizing the traffic jam efficiently in sensing the flux difference of leading sites.